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Differentiate Sin ( 2 Sin − 1 X ) ? - Mathematics

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प्रश्न

Differentiate \[\sin \left( 2 \sin^{- 1} x \right)\] ?

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उत्तर

\[\text{ Let } y = \sin\left( 2 \sin^{- 1} x \right)\]

Differentiate it with respect to we get,

\[\frac{d y}{d x} = \frac{d}{dx}\left[ \sin\left( 2 \sin^{- 1} x \right) \right]\]

\[ = \cos\left( 2 \sin^{- 1} x \right)\frac{d}{dx}\left( 2 \sin^{- 1} x \right) \left[ \text{Using chain rule} \right]\]

\[ = \cos\left( 2 \sin^{- 1} x \right) \times 2\frac{1}{\sqrt{1 - x^2}}\]

\[ = \frac{2\cos\left( 2 \sin^{- 1} x \right)}{\sqrt{1 - x^2}}\]

\[So, \frac{d}{dx}\left[ \sin\left( 2 \sin^{- 1} x \right) \right] = \frac{2\cos\left( 2 \sin^{- 1} x \right)}{\sqrt{1 - x^2}}\]

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अध्याय 11: Differentiation - Exercise 11.02 [पृष्ठ ३७]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 11 Differentiation
Exercise 11.02 | Q 35 | पृष्ठ ३७

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